Question

The second and third terms of an arithmetic progression are 7 and 5 . What is its first term? ​

Answer 1

Answer :

first term, a = 9

Step-by-step explanation :

$\underline{\underline{\bf Arithmetic \ Progression:}}$

• It is the sequence of numbers such that the difference between any two successive numbers is constant.

• In AP,

      a - first term

      d - common difference

      aₙ - nth term

      Sₙ - sum of n terms

• General form of AP,

         a , a+d , a+2d , a+3d , ..........

•  Formulae :-

          nth term of AP,

            $\boxed{\bf a_n=a+(n-1)d}$

             

        Sum of n terms in AP,

            $\boxed{\bf S_n=\frac{n}{2}[2a+(n-1)d}$

__________________________

Given,

• second term, a₂ = 7
• third term, a₃ = 5

To find,

• first term, a = ?

=> common difference, d = a₃ - a₂

                                          = 5 - 7

                                          = -2

Second term,

       a₂ = a + (2 - 1)d

       7 = a + (-2)

       7 = a - 2

       a = 7 + 2

       a = 9

Verification,

 a₃ = a + (3-1)d

     = 9 + 2(-2)

     = 9 - 4

     = 5 ✔

∴ First term, a = 9